Title

Student Author(s)

Faculty Mentor(s)

Dr. Brian Yurk, Hope CollegeDr. Edward Hansen, Hope College

Document Type

Poster

Event Date

4-13-2012

Abstract

Marram grass (Ammophila breviligulata) is a dune pioneer species that thrives with burial by sand. It plays a critical role in controlling the growth and migration of coastal dunes because it anchors the surface with its roots and slows the wind, reducing erosion. As a first step in developing a general mathematical model for sand dune migration, we developed models of marram grass population dynamics. In the simplest case, we used a nonlinear difference equation to account for the effects of burial on population growth rate. This model predicts that the population will evolve to a stable steady state at low values of burial and will undergo periodic behavior at high levels of burial. We expanded this model into a system of nonlinear difference equations by incorporating an equation describing soil quality degradation due to the presence of plants (plants consume soil nutrients, take up space, and introduce harmful microbes) and soil quality improvement due to the influx of fresh sediment (burial). Population growth rate is then determined by the soil quality and plant density. In this case, we found plant-free and plant-present steady states and determined their stability under different burial conditions. We discovered that our equilibrium plant population has a critical point, implying there is a maximum equilibrium population of plants. Using \sc{Matlab} we simulated several scenarios, suggested by our steady state analysis, by changing soil quality parameters and the relative amounts of burial and effective soil depth. In our final model we incorporate spatial dynamics by extending our nonlinear difference equation model to a system of integro-difference equations. This model accounts for the plants ability to spread out horizontally through reproduction.